Properties

Label 12675.p
Number of curves $1$
Conductor $12675$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 12675.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12675.p1 12675z1 \([1, 0, 0, -7693, -270778]\) \(-417267265/19773\) \(-2386012358925\) \([]\) \(24192\) \(1.1378\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12675.p1 has rank \(0\).

Complex multiplication

The elliptic curves in class 12675.p do not have complex multiplication.

Modular form 12675.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + 3 q^{7} + 3 q^{8} + q^{9} + q^{11} - q^{12} - 3 q^{14} - q^{16} - 5 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display